Phase I used Monte Carlo methods to study closed surfaces ("enclosures") with walls that emit beta particles according to Lambert's law. Evacuated Lambertian enclosures should deliver an areally-uniform surface dose to bodies placed within them or apposed to windows in the wall, with little dependence on the size, shape and location of the body in the internal-target case; this approximate constancy should not be seriously worsened - and may indeed be enhanced - by the presence of air. It was shown that scattering in beta-lining of practical thicknesses can produce acceptable flux-uniformity in air-filled spheres of radius 10 to 40 cm. The fluxes can be controllable skewed towards or away from the sphere center by modifying the source configuration. The calculations further show that the resulting surface dose-distribution on spherical targets asymmetrically placed, as well as non-spherical targets symmetrically placed within the enclosures, can be made quite uniform. Phase II will further examine the effect of the pre-insertion flux on surface dose and will experimentally confirm the calculations, mainly by thermoluminescence dosimetry. Enclosures will then be designed to deliver uniform surface doses independent of target size, shape and placement.